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(Sequential truel) Each of persons A, B, and C has a gun contain- ing a single bullet. Each person, as long as she is alive, may shoot at any surviving person. First A can shoot, then B (if still alive), then C (if still alive). (As in the previous exercise, you may interpret the players as political candidates. In this exercise, each candidate has a budget sufficient to launch a negative campaign to discredit exactly one of its rivals.) Denote by pi the probability that player i hits her intended target; assume that 0 pi 1. Assume that each player wishes to maximize her probability of survival; among outcomes in which her survival probability is the same, she wants the danger posed by any other survivors to be as small as possible. (The last assumption is intended to capture the idea that there is some chance that further rounds of shooting may occur, though the possibility of such rounds is not incorporated explicitly into the game.) Model this situation as an extensive game with perfect information and chance moves. (Draw a diagram. Note that the subgames following histories in which A misses her intended target are the same.) Find the subgame perfect equilibria of the game. (Consider only cases in which pA, pB, and pC are all different.) Explain the logic behind A's equi- librium action. Show that "weakness is strength" for C: she is better off if pC pB than if pC > pB.
Now consider the variant in which each player, on her turn, has the additional option of shooting into the air. Find the subgame perfect equilibria of this game when pA pB. Explain the logic behind A's equilibrium action.
Choose a variable from your own organization. describe how calculating a confidence interval from the results of a sample might be useful for learning more about the population statistics for that variable. Indicate whether you would be calculatin..
Compare the people's comfort in the equilibria of the two games. Suppose that each person cares only about her own comfort. Model the situation as a strategic game. Is this game the Prisoner's Dilemma?
Two players, Amy and Beth, take turns choosing numbers; Amy goes first. On her turn, a player may choose any number between 1 and 10 Who will win the game? What are the optimal strategies (complete plans of action) for each player?
A dentist sees about fifteen new patients per month (the rest of her patients are repeats). She knows that on average, over the past year, about half of her patients have needed at least one filling on their first visit.
a consider the same game as in question above but suppose t is not known.instead we know that the game continues with
A poll by Louis Harris and Associates of 1249 adult Americans indicated that 36% believe in ghosts and 37% believe in astrology. Can you compare the proportions using inferential methods for independent binomial samples? If yes, do so. If not, exp..
Identify which player can benefit from making a strategic move, identify the natu re of the strategic move appropriate for this purpose.
What is the dierence between separating and pooling equilibria in this model? Find the separating equilibrium with the lowest possible education level for the high type and What is the largest level of education that can be chosen by workers with..
A survey of 356 local drivers reveals that 18.7% of them car pool. Is there evidence that the actual proportion of local commuters car-pooling is less than national level. Also find and interpret the p-value of this test.
Pertaining to the matrix need simple and short answers, Find (a) the strategies of the firm (b) where will the firm end up in the matrix equilibrium (c) whether the firm face the prisoner’s dilemma.
If so, find a payoff function consistent with the information. If not, show why not. Answer the same questions when, alternatively, the decision-maker prefers the lottery.
Explain to player four why his guess was strictly dominated by another guess - Explicitly check every condition that you need to check to show that s' Pareto dominates s.
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